Express this quotient in scientific notation: ${\frac{2.360\times 10^{-2}} {4.0\times 10^{-3}}}$
Explanation: Start by collecting like terms together. $= {\frac{2.360} {4.0}} \times{\frac{10^{-2}} {10^{-3}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.59 \times 10^{-2\,-\,-3}$ $= 0.59 \times 10^{1}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.59$ is the same as $5.90 \div 10$ , or $5.90 \times 10^{-1}$ $ = {5.90 \times 10^{-1}} \times 10^{1} $ $= 5.90\times 10^{0}$